agitate vs push

agitate is not a noun while push is a noun.

Word	Noun	Adjective	Verb	Adverb
agitate	No	No	Yes	No
push	Yes	No	Yes	No

As verbs, agitate and push are synonyms defined as:

agitate and push: exert oneself continuously, vigorously, or obtrusively to gain an end or engage in a crusade for a certain cause or person; be an advocate for

Other synonyms of agitate include campaign, crusade, fight, press.

As verbs, push is a hypernym of agitate; that is, push is a word with a broader meaning than agitate:

agitate: exert oneself continuously, vigorously, or obtrusively to gain an end or engage in a crusade for a certain cause or person; be an advocate for
push: make publicity for; try to sell (a product)

Other hypernyms of agitate include advertise, advertize, promote.

agitate (noun)	push (noun)
	the act of applying force in order to move something away
	an effort to advance
	an electrical switch operated by pressing
	enterprising or ambitious drive
	the force used in pushing

agitate (verb)	push (verb)
change the arrangement or position of	make publicity for; try to sell (a product)
cause to be agitated, excited, or roused	press, drive, or impel (someone) to action or completion of an action
move very slightly	make strenuous pushing movements during birth to expel the baby
move or cause to move back and forth	move with force
try to stir up public opinion	approach a certain age or speed
exert oneself continuously, vigorously, or obtrusively to gain an end or engage in a crusade for a certain cause or person; be an advocate for	press against forcefully without moving
	move strenuously and with effort
	sell or promote the sale of (illegal goods such as drugs)
	strive and make an effort to reach a goal
	exert oneself continuously, vigorously, or obtrusively to gain an end or engage in a crusade for a certain cause or person; be an advocate for